Early heliocentric systems

  By the IV century B.C. observations had shown that there are two types of stars: fixed stars whose relative position remained constant, and ``wandering stars'', or planets, whose position relative to the fixed stars changed regularly. Fixed stars moved as if fixed to a sphere that turned with the earth at its center, the planets moved about these fixed stars driven by an unknown agency. In fact, Plato regarded the investigation of the rules that determined the motion of the planets as a very pressing research problem.

A remarkable answer was provided by the heliocentric (!!) system of Aristarchus of Samos. Using a clever geometric argument Aristarchus estimated the size of the Sun and concluded it must be enormously larger than the Earth; he then argued that it was inconceivable that such a behemoth would slavishly circle a puny object like the Earth. Once he concluded this, he concluded that the Earth must rotate on its axis in order to explain the (apparent) motion of the stars. Thus Aristarchus conceived the main ingredients of the Copernican system 17 centuries before the birth of Copernicus! Unfortunately these views were soundly rejected by Aristotle: if the Earth is rotating, how is it that an object thrown upwards falls on the same place? How come this rotation does not generate a very strong wind? Due to arguments such as this the heliocentric theory was almost universally rejected until Copernicus' answered these criticisms.

Astronomy also progressed, with the most striking result, due to Eratosthenes, was accurate measurement of the Earth's circumference (the fact that the Earth is round was common knowledge) He noted that the distance from Alexandria to Aswan is 5,000 stadia and that when the sun casts no shadow in Alexandria it casts a shadow corresponding to an angle of 7.2^o (see Fig. 2.10). From this he determined the circumference of the Earth less than 2% accuracy!

 

Figure 2.10: Description of Eratosthenes' procedure for measuring the Earth. He reasoned that the change in angle of the shadow was caused by moving about the Earth. By measuring the angle of the shadow at Seyene, and then in a city that was directly north of Seyene (Alexandria), he determined that the two cities were 7 degrees apart. That is to say, out of the 360 degrees needed to travel all the way around the world, the two cities were 360/7 of that distance. Since he knew that the two cities were about 500 miles apart, he concluded that the the Earth must be (360/7)×500 miles in circumference, or roughly 25,000 miles.  

It is important to remember that the realization that the Earth was round was not lost to the following centuries, so that neither Columbus nor any of his (cultivated) contemporaries had any fear of falling off the edge of the world when traveling West trying to reach the Indies. The controversy surrounding Columbus' trip was due to a disagreement on the size of the Earth. Columbus had, in fact, seriously underestimated the radius of the Earth and so believed that the tiny ships he would command had a fair chance of getting to their destination. He was, of course, unaware of the interloping piece of land we now call America, had this continent not existed, Columbus and his crew would have perished miserably in the middle of the ocean.